Analytical Methods for Squaring the Disc
Fuente:
arXiv
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| Format: | Preprint |
| Published: |
2015
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| _version_ | 1866916542088740864 |
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| author | Fong, Chamberlain |
| author_facet | Fong, Chamberlain |
| contents | We present and discuss several old and new methods for mapping a circular disc to a square. In particular, we present analytical expressions for mapping each point (u,v) inside the circular disc to a point (x,y) inside a square region. Ideally, we want the mapping to be smooth and invertible. In addition, we put emphasis on mappings with desirable properties. These include conformal, equiareal, and radially-constrained mappings. Finally, we present applications to logo design, panoramic photography, and hyperbolic art. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1509_06344 |
| institution | arXiv |
| publishDate | 2015 |
| record_format | arxiv |
| spellingShingle | Analytical Methods for Squaring the Disc Fong, Chamberlain History and Overview Differential Geometry We present and discuss several old and new methods for mapping a circular disc to a square. In particular, we present analytical expressions for mapping each point (u,v) inside the circular disc to a point (x,y) inside a square region. Ideally, we want the mapping to be smooth and invertible. In addition, we put emphasis on mappings with desirable properties. These include conformal, equiareal, and radially-constrained mappings. Finally, we present applications to logo design, panoramic photography, and hyperbolic art. |
| title | Analytical Methods for Squaring the Disc |
| topic | History and Overview Differential Geometry |
| url | https://arxiv.org/abs/1509.06344 |